ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of Ba(Si3N4)2 (Materials Project id mp-567771)

       266       83       75        0        0        0  
        83      315       63        0        0        0  
        75       63      352        0        0        0  
         0        0        0       76        0        0  
         0        0        0        0      130        0  
         0        0        0        0        0       89  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 152.78 GPaEV = 259.19 GPaGV = 106.47 GPaνV = 0.21725
ReussKR = 151.69 GPaER = 248.34 GPaGR = 101.19 GPaνR = 0.22715
HillKH = 152.23 GPaEH = 253.78 GPaGH = 103.83 GPaνH = 0.22216

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
76 GPa 89 GPa 130 GPa 199.05 GPa 272.4 GPa 461.55 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 211.19 GPa 325.43 GPa 1.9169 TPa–1 2.5583 TPa–1 76 GPa 134.57 GPa0.102970.39429Value
Anisotropy 1.541 1.3346 1.771 3.8291Anisotropy
Axis 0.0000
0.7340
0.6792
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
0.0002
0.7071
-0.7071
0.7055
0.4402
-0.5554
0.2994
0.6821
-0.6671
Axis
-0.0000
1.0000
0.0000
0.0001
-0.7071
-0.7071
-0.6929
0.2640
-0.6709
-0.1983
0.7284
0.6558
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane